About this book
The canonical way to establish the central limit theorem for i.i.d. random variables is to use characteristic functions and Lévy’s continuity theorem. This monograph focuses on this characteristic function approach and presents a renormalization theory called mod-ϕ convergence. This type of convergence is a relatively new concept with many deep ramifications, and has not previously been published in a single accessible volume. The authors construct an extremely flexible framework using this concept in order to study limit theorems and large deviations for a number of probabilistic models related to classical probability, combinatorics, non-commutative random variables, as well as geometric and number-theoretical objects.
Intended for researchers in probability theory, the text is carefully well-written and well-structured, containing a great amount of detail and interesting examples.
Probability Theory Number Theory Combinatorics Matrix Theory Deviations
- DOI https://doi.org/10.1007/978-3-319-46822-8
- Copyright Information The Author(s) 2016
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-46821-1
- Online ISBN 978-3-319-46822-8
- Series Print ISSN 2365-4333
- Series Online ISSN 2365-4341
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